```Date: Jan 16, 2013 3:34 AM
Author: Jussi Piitulainen
Subject: Re: simplifying rational expressions

stony writes:> Need a little help with this.  We are simplifying the following, but> the solution is pretty lengthy and messy because of the enormous> number of factors.  I was thinking that may be I am missing seeing a> pattern (some series or something).  Is grunt work the only way to> solve this or is there a pattern that can simplify the whole process?> > My daughter was trying to solve this, but ended up with the mess and> then I got the same mess, but I thought there may be an easy way to> simplify this that I may be missing.> > ((b-c)/((a-b)(a-c)))  +  ((c-a)/((b-c)(b-a))) + ((a-b)/((c-a)(c-b))) +> (2/(b-a)) - (2/(c-a))> > of course, I took all the factors in the denominator and then started> multiplying the numerator with the remaining factors to end up with a> mess.  I suspect you are missing the fact that (a - b) and (b - a) in thedenominators are essentially the same factor. The common denominatorof the terms is (a - b)(a - c)(b - c). I think you can leave thedenominator in that form.I did the numerator two ways: in terms of these same factors, andmultiplying out and combining terms. They seemed about equally simpleto me, though I may have made mistakes. I usually do. Be careful withthe signs :)Hope this helps.
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